A fact is a statistic, datum, or event that is objective, observable, and recordable.
Facts are used as evidence to make claims. Facts are generally held to be mind-independent, i.e. they would continue to be the case whether or not anyone believed them, or indeed whether or not there were any minds to believe them in the first place.
Facts are different from theories, which attempt to explain trends in facts. Facts are also different from opinions, which are subjective interpretations of facts.
In history and journalism, "facts" refer to recorded, independently-verifiable events or statistics. In science, "facts" are observations or data, (fact: at sea-level, water boils at 100 degrees Celsius, while other liquids boil at different temperatures) and theories are built to explain facts (theory: why water boils at 100 C, why different liquids have different boiling points).
During The 18th century Enlightenment, the statement "facts are stubborn things" was widely repeated. It encapsulates an Enlightenment belief that incontrovertible empirical data could be found on any question and that such facts would irresistibly lead public opinion in an enlightened direction by dispelling the mystifications and superstitions of earlier, barbarous ages. In the Early Republic in the United States, the phrase was often directed against the allegedly dangerous speculations and innovations of Jacobin-Jeffersonian philosophy.
There is some evidence that human psychology is such that facts often do not drive beliefs as much as beliefs drive one's willingness to listen to certain facts.
For example, it is an opinion that the homosexual agenda is not harmful, while it is a fact that the average gay man has a life expectancy far less than that of a straight man.
Quotes About Facts
John Adams wrote: "Facts are stubborn things; and whatever may be our wishes, our inclinations, or the dictates of our passion, they cannot alter the state of facts and evidence." 
"The pure and simple truth is rarely pure and never simple." -- Oscar Wilde
"First get your facts; then you can distort them at your leisure." -- Mark Twain
"We all know that facts have a liberal bias." -- Stephen Colbert
- Pasley, Jeff. "Department of Not Giving John Adams Too Much Credit" in Common-Place (july 2009) online; shows the slogan was very widely used in the 18th century.